Two cells of emfs 1.5 V and 2.0 V, having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.

Solution

Given,
EMF, E₁ = 1.5 V ; E₂ = 2 V
Internal resistance, r = 0.2 $straight capital omega space nd space 0.3 space straight capital omega$
Effective emf of two cells connected in parallel is,
E_eff = $fraction numerator straight E subscript 1 straight r subscript 2 space plus space straight E subscript 2 straight r subscript 1 over denominator straight r subscript 1 space plus space straight r subscript 2 end fraction$
This implies,
$straight E subscript eff space equals space fraction numerator 1.5 space straight x space 0.3 space plus space 2.0 space straight x space 0.2 over denominator 0.5 end fraction space equals space 1.7 space straight V$
The effective resistance can be calculated as:
R_eff = $fraction numerator straight r subscript 1 straight r subscript 2 over denominator straight r subscript 1 space plus space straight r subscript 2 end fraction$
That is,
R_eff = $fraction numerator 0.2 space straight x space 0.3 over denominator 0.5 end fraction space equals space 0.12 space capital omega$

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Current Electricity

Two cells of emfs 1.5 V and 2.0 V, having internal resistances 0.2 Ω and 0.3 Ω, respectively, are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.

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